Question

How many different three letter initials can a person have, if the first and last initial

cannot be the same?

*note: i'm pretty sure the answer looks something like 26!/(???). I'm supposed to understand this using factorials. I don't understand how to get the denominator.

Answer 1

26*26*25 = 16,900

Explanation:

First, we focus on the first initial, we have 26 letters that could fit in (the whole alphabet).

In the last initial we can't have the same we have in the first one, so we have 25 letters (the whole alphabet minus the letter that we already choose in the first initial ).

We have no restrictions for the middle one, so again we have 26 letters that could fit in.

So, we have 26*26*25 combinations (we multiply them because they happen all at the same time)

There is no need to use factorials, but we can use them if you want to.

Let's notice that 26! = 26*25*24*23*22*...

In our calculation, we only need the two first factors, so we can divide by 24! =24*23*22*21*...

Therefore,

26*26*25 = 26 * 26! /24!